Model dielectric functions for ion stopping: The relation between their shell corrections, plasmon dispersion and Compton profiles

We describe a set of energy (ω) and momentum (q)-dependent dielectric functions with the same shape of the loss function (Im−1/ϵ(ω,q)) in the optical limit (q = 0) and thus the same mean ionization energy I but different behavior away from q = 0. The corresponding proton stopping values differ especially at lower energies. Within the Bethe formula the stopping only depends on the mean excitation energy I. These models display thus different shell corrections, defined as the deviation from the stopping from the Bethe values. Shell-correction contributions originate equally from collisions with low momentum transfer and with high momentum transfer. Intermediate q collisions do not contribute to the shell corrections. At high q the shell corrections are related to the width of the loss function at these q values (which is proportional to the momentum distribution of the electrons [“Compton profiles”]) or, for classical models, from a shift in position. The low-q contribution is related to the plasmon dispersion.